Light Bulbs in Series and in Parallel. Two light bulbs have constant resistances of 400Ω and 800Ω. The two light bulbs are connected in series across a 120-V line. Afterwards, the two light bulbs are connected in parallel across the 120-V line. (h) In which situation is there a greater total light output from both bulbs combined?

Verified step by step guidance

1. Calculate the total resistance when the bulbs are connected in series. Use the formula for resistors in series: R_{total} = R_1 + R_2, where R_1 and R_2 are the resistances of the two bulbs.
2. Calculate the total current flowing through the circuit when the bulbs are connected in series using Ohm's Law: I = V / R_{total}, where V is the voltage of the line.
3. Calculate the total resistance when the bulbs are connected in parallel. Use the formula for resistors in parallel: 1/R_{total} = 1/R_1 + 1/R_2.
4. Calculate the total current flowing through the circuit when the bulbs are connected in parallel using Ohm's Law: I = V / R_{total}.
5. Compare the total power dissipated by the bulbs in each configuration using the formula P = VI, where P is the power, V is the voltage, and I is the current calculated in the previous steps. The configuration with the higher power dissipation will have a greater total light output.

Key Concepts

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship is expressed as V = IR. Understanding Ohm's Law is crucial for analyzing how voltage, current, and resistance interact in electrical circuits, particularly when determining the behavior of light bulbs in series and parallel configurations.

Series and Parallel Circuits

In a series circuit, components are connected end-to-end, so the same current flows through each component, and the total resistance is the sum of individual resistances. In contrast, in a parallel circuit, components are connected across the same voltage source, allowing multiple paths for current to flow, which results in a lower total resistance. The arrangement of light bulbs in series or parallel affects the total current and voltage distribution, influencing their brightness and overall light output.

Power in Electrical Circuits

The power (P) consumed by an electrical device is calculated using the formula P = IV, where I is the current and V is the voltage. In resistive loads like light bulbs, power can also be expressed as P = I²R or P = V²/R. The total power output from multiple bulbs can be compared in series and parallel configurations, as the arrangement affects both the current through each bulb and the total power consumed, ultimately determining the light output.